Variations in energy of cyclotron lines with double structures formed in a line-forming region with bulk motion in accreting X-ray pulsars

Abstract

Abstract We show that variations in the energy of a cyclotron resonant scattering feature with luminosity can be explained by considering a variation of the bulk velocity of infalling matter in the two-dimensional structure of an accretion column. Variations in the energy of a cyclotron line with luminosity are computed by taking into account the variation in gradient of the bulk velocity with luminosity in a line-forming region. We mainly discuss the positive correlation between the energy of the cyclotron line $E_{cyc}$ at the fundamental and the luminosity as observed in the spectra of GX 304−1, A0535+262, and Vela X-1, considering a change in gradient of the bulk velocity in the line-forming region with luminosity in addition to a change of altitude of the line-forming region with luminosity. Consequently, we demonstrate that the change in the observed line energy with luminosity can be successfully reproduced by a variation in bulk velocity due to radiation pressure as well as the altitude of an accretion mound.